How this calculation works
Retain the initial current as the inductor state, solve the first-order closed-loop response, and keep passive-sign resistor and inductor voltage references consistent.
τ = L/R; I(t) = Vs/R + (I0 − Vs/R)e^(−t/τ); VL = Vs − IRA worked example
10 Ω and 100 mH give τ = 0.01 s. Starting at 0 A toward a 12 V source gives about 0.758545 A at 0.01 s, with resistor and inductor voltages summing to 12 V.
Good to know
One ideal R and L with a fixed ideal DC source and closed current path. No saturation, parasitics, winding loss beyond entered resistance or rating selection. Source-zero decay does not mean an open-circuited inductor. Tails beyond 1,000τ use numerical zero.
Reference: Reference: model definitions and scope (opens in a new tab) ↗
Inductor current is the state that carries across the switch
The default 100 mH and 10 Ω give a 0.01-second time constant. Starting at zero current with a fixed 12 V source, the long-term ideal current is 1.2 A. At one time constant, current is about 0.758545 A.
At that instant, the resistor voltage is about 7.585447 V and the inductor voltage about 4.414553 V. They sum to 12 V in the chosen passive reference. An inductor can have a voltage while its current changes; replacing it with its eventual DC short at time zero would discard the transient.
The RC time constant calculator follows capacitor voltage, whereas the RL transient retains initial inductor current and a closed current path.
Zero source means a closed decay path in this model
Set the source to zero and the initial current to 2 A. Through the same 10 Ω and 100 mH, current after one time constant is about 0.735759 A. The resistor drop is positive in the current reference while the inductor voltage is negative, supplying the resistive loss from stored magnetic energy.
This is a closed resistor/inductor loop. Opening an inductor circuit is a different switching problem, with parasitic paths and voltage behavior not represented here. No arc, snubber, protection circuit or component-rating selection is inferred from the source-zero calculation.
A time constant is not an exact settling time
After one time constant, about 36.788% of the initial difference from steady current remains. After five, about 0.6738% remains. If initial current already equals the steady value, the ideal current is constant from the start and the initial error is zero.
The RC time constant calculator follows capacitor voltage in another first-order model. The series RLC damping calculator adds a second energy-storage element and a different response regime. Here the source and components are fixed, with no saturation, core loss or winding resistance beyond the entered total R.
A few questions, answered
Is the RL time constant RC or L/R?
It is L/R, with L in henries and R in ohms.
Can the initial current be nonzero?
Yes. It is explicitly retained in the exponential solution.
Can inductor voltage be negative during decay?
Yes. With the stated passive reference, it can return stored magnetic energy while resistor voltage remains along the current.
Does a zero source simulate an open switch?
No. It represents a closed RL decay path with zero applied source.